We present LTE and NLTE results on the formation of LiI lines (λ6103, λ6708, and λ8126) in the atmospheres of solar metallicity dwarfs with effective temperatures in the range 5500K to 2000K. NLTE effects are governed by overionization of Li and by the interlocking effects of energy levels. For stars with T_eff_>=4000K, we confirm previous findings by Magazzu et al. (1992). NLTE corrections can lower the LTE Li abundances derived from strong LiIλ6708 lines by up to 0.5 dex. Our computations using model atmospheres with T_eff_ between 3000K and 2000K show that prominent LiI lines are formed. We give a set of line profiles, which support the feasability of the Li test for brown dwarfs. The ionization-dissociation equilibrium for Li species was carefully considered. NLTE effects on the LiI lines of very cool dwarfs are found to be small, implying corrections to the LTE Li abundances lower than 0.1 dex. Several numerical tests have been carried out to estimate the effects of chromosphere-like structures on the formation of LiI lines. Our preliminary results suggest that in the presence of very strong chromospheres, the line strengths are reduced.